Number systems over orders
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XYX" target="_blank" >RIV/61988987:17310/18:A1901XYX - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00605-018-1191-x" target="_blank" >http://dx.doi.org/10.1007/s00605-018-1191-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00605-018-1191-x" target="_blank" >10.1007/s00605-018-1191-x</a>
Alternative languages
Result language
angličtina
Original language name
Number systems over orders
Original language description
LetKbe a number field of degree k and letObe an order inK. Ageneralized number system over O GNS for short) is a pair p, D) where p. O[x] is monic and D. O is a complete residue system modulo p0) containing 0. If each a. O[x] admits a representation of the form a = - 1 j= 0 dj x j mod p) with . N and d0,..., d - 1. D then the GNS p, D) is said to have the finiteness property. To a given fundamental domain F of the action of Zk on Rk we associate a class GF := {p, DF) : p. O[x]} of GNS whose digit sets DF are defined in terms of F in a natural way. We are able to prove general results on the finiteness property of GNS in GF by giving an abstract version of the well- known " dominant condition" on the absolute coefficient p0) of p. In particular, depending on mild conditions on the topology of F we characterize the finiteness property of px +/- m), DF) for fixed p and large m. N. Using our new theory, we are able to give general results on the connection between power integral bases of number fields and GNS.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MONATSH MATH
ISSN
0026-9255
e-ISSN
1436-5081
Volume of the periodical
187
Issue of the periodical within the volume
4
Country of publishing house
AT - AUSTRIA
Number of pages
24
Pages from-to
681-704
UT code for WoS article
000446558400006
EID of the result in the Scopus database
2-s2.0-85047154745